Investigations into real determinantal quartic hypersurfaces
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- Matematisk institutt [3782]
Abstract
This thesis is a collection of four papers about symmetric and Hermitian determinantal representations of quartic hypersurfaces. - Paper I classifies rational quartic symmetroids in 3-space. - Paper II classifies rational quartic spectrahedra in 3-space. - Paper III finds the maximal dimension for a quartic symmetroid which is singular along a quadric of codimension 1. - Paper IV gives a bound on the number of isolated essential singularities on a quartic surface with a determinantal representation. A conjecture is formulated about the configurations of isolated essential singularities on quartic surfaces with a Hermitian determinantal representation and a nonempty spectrahedron.List of papers
Paper I: Helsø, M. ‘Rational quartic symmetroids’. In: Adv. Geom. Vol. 20, no. 1 (2020), pp. 71–89. Included in the thesis. Published version can be found here: https://doi.org/10.1515/advgeom-2018-0037 |
Paper II: Helsø, M., & Ranestad, K. (2021). Rational quartic spectrahedra. Mathematica Scandinavica, 127(1), 79-99. Included in the thesis. Published version can be found here: https://doi.org/10.7146/math.scand.a-121456 |
Paper III: Helsø, M. ‘Maximal dimension of quartic symmetroids with a double quadric of codimension 1’. 2019. Included in the thesis. Pre-print can also be found here: https://arxiv.org/abs/1905.01091 |
Paper IV: Helsø, M. ‘Determinantal quartic surfaces with a definite Hermitian representation’. 2020. Included in the thesis. Pre-print can also be found here: https://arxiv.org/abs/2007.01121 |